Theorem 2 ([1]}) 
Any proper lower semicontinuous function \(f:\mathbb {R}^n\Rightarrow \mathbb {R}\cup \lbrace +\infty \rbrace \)  that is definable in an o-minimal structure \(\Delta \)  has the KL property at each point of \(\operatorname{dom}\partial f\) . Moreover, the function \(\psi \)  is definable in \(\Delta \) .

